Question
Find a, b, c if the matrix $A=\left[\begin{array}{ccc}2 & a & 3 \\ -7 & 4 & 5 \\ c & b & 6\end{array}\right]$ is a symmetric matrix.
✓
Answer
Given that $\mathrm{A}=\left[\begin{array}{ccc}2 & a & 3 \\ -7 & 4 & 5 \\ \mathrm{c} & \mathrm{b} & 6\end{array}\right]$ is a symmetric matrix.
$a_{i j=} a_{j i}$ for all $i$ and $j$
As $a_{12}=a_{21}$
$\therefore \quad a=-7$
As $a_{32}=a_{23}$
$
\therefore \mathrm{b}=5
$
As $a_{31}=a_{13}$
$
\therefore \mathrm{c}=3
$
$a_{i j=} a_{j i}$ for all $i$ and $j$
As $a_{12}=a_{21}$
$\therefore \quad a=-7$
As $a_{32}=a_{23}$
$
\therefore \mathrm{b}=5
$
As $a_{31}=a_{13}$
$
\therefore \mathrm{c}=3
$
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